Relation between the correlation dimensions of multifractal wave functions and spectral measures in integer quantum Hall systems

We study the time evolution of wave packets of noninteracting electrons in a two-dimensional disordered system in strong magnetic field. For wave packets built from states near the metal-insulator transition in the center of the lowest Landau band we find that the return probability to the origin p(t) decays algebraically, p(t)∼${\mathit{t}}_2^{\mathrm{-}\mathit{D}}$/2, with a nonconventional exponent ${\mathit{D}}_2$/2. ${\mathit{D}}_2$ is the generalized dimension describing the scaling of the second moment of the wave function. We show that the corresponding spectral measure is multifractal and that the exponent ${\mathit{D}}_2$/2 equals the generalized dimension D${\mathrm{̃}}_2$ of the spectral measure.